1. 1-5 Simplifying Algebraic Expressions Do Now Evaluate each algebraic expression for y = 3. 1.3y + y2. 7y 3. 10y – 4y4. 5y 2 + y - 2 12 21 18 46

2. 1-5 Simplifying Algebraic Expressions Learn to identify like terms and simplify algebraic expressions. Goal:

3. 1-5 Simplifying Algebraic Expressions In the algebraic expression 5y 2 + y - 2, 5y 2, y, and 2 are called terms. A term can be a number (constant), a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. 5y 2 + y - 2 term

4. 1-5 Simplifying Algebraic Expressions In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. Coefficient Variable

5. 1-5 Simplifying Algebraic Expressions Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants are also like terms. Like Terms Unlike Terms 3x and 2x 5x 2 and 2x The exponents are different. 3.2 and n Only one term contains a variable 6a and 6b The variables are different w 2 and 3w 2 5 and 1.8

6. 1-5 Simplifying Algebraic Expressions Identify like terms in the list. Example A 3t 5w 2 7t 9v 4w 2 8v Look for like variables with like powers. 3t 5w 2 7t 9v 4w 2 8v Like terms: 3t and 7t 5w 2 and 4w 2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

7. 1-5 Simplifying Algebraic Expressions Identify like terms in the list. 2x 4y 3 8x 5z 5y 3 8z Look for like variables with like powers. Like terms: 2x and 8x 4y 3 and 5y 3 5z and 8z 2x 4y 3 8x 5z 5y 3 8z

8. 1-5 Simplifying Algebraic Expressions x Combining like terms is like grouping similar objects. += x x x xx x xx xxxx x xxxx 4x4x+5x5x =9x9x To combine like terms that have variables, add or subtract the coefficients.

9. 1-5 Simplifying Algebraic Expressions Simplify the algebraic expressions. Example B 6t – 4t 2t2t 6t and 4t are like terms. Subtract the coefficients. 45x – 37y + 87 In this expression, there are no like terms to combine.

10. 1-5 Simplifying Algebraic Expressions Example B 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 5a 2 + b + 11b 2 – 6 Identify like terms. Add or subtract the coefficients. (3a 2 + 2a 2 ) + (5b – 4b) + 11b 2 – 6 Group like terms. Simplify the algebraic expressions.

11. 1-5 Simplifying Algebraic Expressions Simplify the algebraic expressions. 2(x 2 – 13x) + 6 There are no like terms to combine. 2x – 26x + 6 2 Distributive Property. Example B

12. 1-5 Simplifying Algebraic Expressions Practice on your own: Simplify the algebraic expressions.

13. 1-5 Simplifying Algebraic Expressions Write an expression for the perimeter of the triangle. Then simplify the expression. Extra Example x 2x + 33x + 2 2x + 3 + 3x + 2 + x (x + 3x + 2x) + (2 + 3) 6x + 5 Write an expression using the side lengths. Identify and group like terms. Add the coefficients.

14. 1-5 Simplifying Algebraic Expressions x 2x + 1 x + 2x + 1 + 2x + 1 5x + 2 Write an expression using the side lengths. Identify and group like terms. Add the coefficients. Write an expression for the perimeter of the triangle. Then simplify the expression. (x + 2x + 2x) + (1 + 1) Extra Example

15. 1-5 Simplifying Algebraic Expressions Identify like terms in the list. 1. 3n 2 5n 2n 3 8n 2. a 5 2a 2 a 3 3a 4a 2 Simplify the algebraic expression. 3. 4a + 3b + 2a 4. x 2 + 2y + 8x 2 2a 2, 4a 2 5n, 8n 6a + 3b 9x 2 + 2y Lesson Quiz

16. 1-5 Simplifying Algebraic Expressions 5. Write an expression for the perimeter of the given figure. 6x + 8y 2x + 3y x + y Lesson Quiz

17. 1-5 Simplifying Algebraic Expressions 6. Identify the like terms in the list. 6a, 5a 2, 2a, 6a 3, 7a A. 6a and 2a B. 6a, 5a 2, and 6a 3 C. 6a, 2a, and 7a D. 5a 2 and 6a 3 Lesson Quiz

18. 1-5 Simplifying Algebraic Expressions 7. Identify the like terms in the list. 16y 6, 2y 5, 4y 2, 10y, 16y 2 A. 16y 6 and 16y 2 B. 4y 2 and 16y 2 C. 16y 6 and 2y 2 D. 2y 5 and 10y Lesson Quiz